Let $$f(x)$$ be a $$non-negative$$ continuous function such that the area bounded by the curve y $$=f(x)$$, $$X-axis$$ and the ordinates $$x=$$π$$/4$$ and $$x=$$βπ$$/4$$, is $$($$β$$sin$$⁡β$$+$$π$$4cos$$⁡β$$+2$$β$$)$$ then,f$$π$$$$2$$ is equal to

Question

Let $$f(x)$$ be a $$non-negative$$ continuous function such that the area bounded by the curve y $$=f(x)$$, $$X-axis$$ and the ordinates $$x=$$π$$/4$$ and $$x=$$β>π$$/4$$,  is $$($$β$$sin$$⁡β$$+$$π$$4cos$$⁡β$$+2$$β$$)$$ then,f$$π$$$$2$$ is equal to

Infinity Learn · Accepted Answer

We have,∫π$$/4$$β $$f(x)dx=$$β$$sin$$⁡β$$+$$π$$4cos$$⁡β$$+2$$βOn differentiating both sides w.r.t. β (by$$  Leibnitz $$rule), we $$getf($$β$$)=$$β$$cos$$⁡β$$+$$$$sin$$⁡β−π$$4sin$$⁡β$$+2f$$$$π$$$$2=1$$−π$$4+2$$

Let f(x) be a non-negative continuous function such that the area bounded by the curve y =f(x), X-axis and the ordinates $x = π / 4 and x = β > π / 4,$ is $(βsin β + \frac{π}{4} \cos β + \sqrt{2} β)$ then, $f (\frac{π}{2})$ is equal to

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Let f(x) be a non-negative continuous function such that the area bounded by the curve y =f(x), X-axis and the ordinates x=π/4 and x=β>π/4, is (βsin⁡β+π4cos⁡β+2β) then,fπ2 is equal to

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Let f(x) be a non-negative continuous function such that the area bounded by the curve y =f(x), X-axis and the ordinates $x = π / 4 and x = β > π / 4,$ is $(βsin β + \frac{π}{4} \cos β + \sqrt{2} β)$ then, $f (\frac{π}{2})$ is equal to